Advertisements
Advertisements
प्रश्न
If a, b and c are in A.P. show that a + 4, b + 4 and c + 4 are in A.P.
उत्तर
a, b and c are in A.P.
`=>` b – a = c – b
`=>` 2b = a + c
Given terms are (a + 4), (b + 4) and (c + 4)
Now (b + 4) – (a + 4) = b – a
= `(a + c)/2 - a`
= `(a + c - 2a)/2`
= `(c - a)/2`
And (c + 4) – (b + 4) = c – b
= `c - (a + c)/2`
= `(2c - a - c)/2`
= `(c - a)/2`
Since (b + 4) – (a + 4) = (c + 4) – (b + 4), then the given terms are in A.P.
APPEARS IN
संबंधित प्रश्न
Find the common difference and 99th term of the arithmetic progression:
`7 3/4, 9 1/2, 11 1/4, ................`
If tn represents nth term of an A.P., t2 + t5 – t3 = 10 and t2 + t9 = 17, find its first term and its common difference.
Find the value of p, if x, 2x + p and 3x + 6 are in A.P.
If a, b and c are in A.P. show that 4a, 4b and 4c are in A.P.
An A.P. consists of 57 terms of which 7th term is 13 and the last term is 108. Find the 45th term of this A.P.
Which term of A.P 3, 10, 17, .... Will be 84 more than its 13th term?
The sum of the 2nd term and the 7th term of an A.P. is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P.
Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : 2, 4, 8, 16,….
Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms : 12, 32, 52, 72,...
The first term and the common difference of an A.P. are 8 and –5 respectively. The A.P. is ______.
